{
  "id": "1205.3382",
  "version": "v1",
  "published": "2012-05-15T14:18:03.000Z",
  "updated": "2012-05-15T14:18:03.000Z",
  "title": "Microstructural Degeneracy associated with a Two-Point Correlation Function and its Information Content",
  "authors": [
    "Cedric J. Gommes",
    "Yang Jiao",
    "Salvatore Torquato"
  ],
  "comment": "Accepted for publication in Physical Review E",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Two-point correlation functions provide crucial yet incomplete characterization of microstructures because different microstructures may have the same correlation function. In an earlier Letter [Phys. Rev. Lett. 108, 080601 (2012)], we addressed the degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation and additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically an energy profile corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of this profile is a measure of the roughness of the energy landscape, which can be used as a proxy for ground-state degeneracy. The relationship between roughness metric and ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the degeneracy of a variety of microstructures, including hard disks and Poisson point processes as well as those with known degeneracies (single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-15T14:18:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-point correlation function",
      "information content",
      "microstructural degeneracy",
      "ground-state degeneracy",
      "monte carlo algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3382G"
    }
  }
}